Analysis of Peierls-Yoccoz rotational energy of nuclei with semi-realistic interaction

Abstract: The Peierls-Yoccoz (PY) rotational energy of nuclei has been analyzed by the angular-momentum projection (AMP) on the axial Hartree-Fock solutions, by using the semi-realistic effective Hamiltonian M3Y-P6. The rotational energy is decomposed into contributions of the individual terms of the Hamiltonian, and their ratios to the total PY rotational energy are calculated. Except for light or weakly-deformed nuclei, the ratios of the individual terms of the Hamiltonian are insensitive to nuclides and deformation. The contributions of kinetic energies are large and close to the rigid-rotor values, although those of central forces are sizable. For light or weakly-deformed nuclei, the ratios significantly depend on nuclei and deformation. The contributions of noncentral forces are not negligible. Regardless of nuclides, the attractive forces decrease the moment-of-inertia, and the repulsive forces increase it. A general formula for the PY rotational energy is derived, which suggests that higher-order terms of the cumulant expansion play roles in the rotational energy and the moment-of-inertia for light or weakly-deformed nuclei.